It is well-known in traffic flow mathematics that the closer vehicles are spaced together the slower the flow, and this is shown by the general traffic flow principle expressed by the equation:where r(n,m) is the distance between two vehicles, n and m, and dn/dt and dm/dt represent the velocity of the two vehicles: as r(n,m)→0, dn/dt→0 and dm/dt→0 as well.
The main problem in getting a congestive traffic event flowing again is actually the behavior of the drivers themselves. FIGS. 1A–1C show the behavioral characteristics of drivers that cause continued gridlock problems. The main problem is that drivers fail to space themselves apart from a vehicle in front of them (or, in a merge situation, a two-dimensional spacing) when the traffic flow resumes, thus keeping r(n,m) close to 0 at all times. Even if a driver is attempting to space themselves from the leading vehicle, an erratic “dissipation speed” may bunch the two cars again keeping traffic from flowing. FIG. 1A shows a representative traffic event at time T(E) or time of event, the location of the event is shown by a star and labeled P(tc) where the velocity of the representative four vehicles is near zero (v vector =0). FIG. 1B depicts the initial dissipation of the traffic congestion event in FIG. 1A and a chosen t(0) or initial time. In FIG. 1B the distance r(n,m) initially may increase, but as shown in FIG. 1C at time t(0)+i (where i=2 seconds in the illustrative example), r(n,m) is decreased through driver behavior (acceleration (a(n)), not letting a vehicle merge properly, etc.) or other circumstances to decrease distance and leading back to congestion as shown by the bunching in vehicles 3 and 4 and the closing gap between n and m.
FIG. 2 also depicts another type of congestion based on driver habits in a highway merge zone which causes unnecessary slowing and congestion problems. The merges tend to complicated traffic flow both in the merge lanes and the travel lane into which the merge lane flow and the adjacent lanes. In this diagram, velocity x is a threshold velocity which indicates that the travel lane traffic has dropped below a target velocity most-likely due to the problems created by the merge lane traffic. The velocity of the vehicle in the lane adjacent to the travel lane while at a threshold will also likely drop below the threshold if vehicles in the travel lane continue to pull into the adjacent lane from low or stopped velocity.
A way to keep efficient spacing during the dissipation of a traffic congestion event would facilitate traffic flow and reduce the problems caused by driver impatience and other natural occurring traffic events such as merges.